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Found problems: 1

2012 Miklós Schweitzer, 1
Is there any real number $\alpha$ for which there exist two functions $f,g: \mathbb{N} \to \mathbb{N}$ such that $$\alpha=\lim_{n \to \infty} \frac{f(n)}{g(n)},$$ but the function which associates to $n$ the $n$-th decimal digit of $\alpha$ is not recursive?
discrete mathematics recursive real analysis computable analysis algebra